Too Many Angles, Too Little Information

Geometry Level 3

In a triangle \(ABC\), the measures of the angles are \(\angle A=30^\circ,\) \(\angle B=80^\circ.\) Point \(M\) lies inside the triangle, such that \(\angle MAC = 10^\circ,\) \(\angle MCA = 30^\circ.\) What is the measure (in degrees) of \(\angle BMC?\)

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